The invention concerns a rolling-member worm-drive, comprising a spindle having an axis and an outer peripheral surface and a nut element having an inner peripheral surface surrounding the spindle, where at least one nut groove with two end regions, guiding rolling-members and running helically about the axis, is formed in the inner peripheral surface, which groove, together with the outer peripheral surface of the spindle, defines a helical rolling-member screw path running between the two end regions, where in addition this rolling-member screw path is completed by a rolling-member return path running between the two end regions to a closed rolling-member circulation path, where in addition the rolling-member circulation path is occupied by an endless row of rolling-members lying, on the one hand, in the nut groove and, on the other, on a helical race of the outer peripheral surface, each rolling-member being in a ready-to-roll condition, where in addition a rolling-member diverting element is arranged on the nut element in each of the end regions for transfer of the rolling-members between the rolling-member screw path and the rolling-member return path and between the rolling-member return path and the rolling-member screw path, and where the rolling-member diverting element is held on the nut element by means of a securing element.